Missing Values, UNTIE, and Hypothesis Tests

PROC TRANSREG can estimate missing data and monotonically transform variables while untying tied values. Estimates of ordinary missing values (.) are all permitted to be different. Analyses with UNTIE transformations, the UNTIE= a-option, and ordinary missing data estimation are all prone to degeneracy problems. Consider the following example. A perfect fit is found by collapsing all observations except the one with two missing values into a single value in y and x1. The following statements produce Figure 93.60:

```title 'Missing Data';

data x;
input y x1 x2 @@;
datalines;
1 3 7    8 3 9    1 8 6    . . 9    3 3 9
8 5 1    6 7 3    2 7 2    1 8 2    . 9 1
;
```
```proc transreg solve;
model linear(y) = linear(x1 x2);
output;
run;

proc print;
run;
```

Figure 93.60 Missing Values Example
 Missing Data

Obs _TYPE_ _NAME_ y Ty Intercept x1 x2 TIntercept Tx1 Tx2
1 SCORE ROW1 1 2.7680 1 3 7 1 5.1233 7
2 SCORE ROW2 8 2.7680 1 3 9 1 5.1233 9
3 SCORE ROW3 1 2.7680 1 8 6 1 5.1233 6
4 SCORE ROW4 . 12.5878 1 . 9 1 12.7791 9
5 SCORE ROW5 3 2.7680 1 3 9 1 5.1233 9
6 SCORE ROW6 8 2.7680 1 5 1 1 5.1233 1
7 SCORE ROW7 6 2.7680 1 7 3 1 5.1233 3
8 SCORE ROW8 2 2.7680 1 7 2 1 5.1233 2
9 SCORE ROW9 1 2.7680 1 8 2 1 5.1233 2
10 SCORE ROW10 . 2.7680 1 9 1 1 5.1233 1

Generally, the use of ordinary missing data estimation, the UNTIE transformation, and the UNTIE= a-option should be avoided, particularly with hypothesis tests. With these options, parameters are estimated based on only a single observation, and they can exert tremendous influence over the results. Each of these parameters has one model degree of freedom associated with it, so small or zero error degrees of freedom can also be a problem.